A hydraulic fed fire?
I know a wee bit about that situation and have the scars to prove it.
Whether you could fly for long with a fire depends upon the place in the aircraft where the fire is located, whether it is a return line or pressure line that lets go, and what kind of terrain you are flying over and whether you are VMC or IMC.
A simple leak or return line breech makes for a nice polite fire...one that could possibly be dealt with by means of a hand held extinguisher depending upon the location and access by the crew.
When a pressure line lets go and feeds the fire....that is an altogether different event. My fire was in the chin bubble area where the aircraft utility system supplied the brake system. That was a 1500 PSI system with a return pressure of about 125 PSI. I assume the return line was severed first and generated a pretty good fire but a very short while later the pressure line must have gone because that fire filled the left side of the cockpit where I was sitting. Some of the flames were pulled out of the chin bubble area and carried down the left side of the aircraft and actually melted the skin of the aircraft up to 30 feet back.
If the failure would have involved the flight control system operating at a 3000 PSI pressure, the fire would have been horrendous.
We stayed in the air....landing was impossible due to the weather and sheer lack of a clearing to use. We finally got the fire out, probably because the utility system had exhausted its contents.
Trust me when I say.....you do not ever want to have that kind of experience but if you do....land as quickly as you can.
I can assure you a flight control system failure on a 2500-3500 PSI system would cause a catastrophic fire.